ON SOME RESULTS OF NUMBER THEORETIC TRANSFORM (NTT) -PERIODIC SIGNAL
Résumé
The interest givento the application of Number Theoretic Transforms (NTT’s)to digital signal processing has not cease
grow. These transformations are used to improve convolutions, where arithmetic operations give a modulo an integerres
In order to understand the domain of the NTT, we have to show their powerful properties and exploit them in diffe
applications such as in signal processing.
Références
[1] E. O. BRIGHA, “The Fast Fourier Transform”.
Prentice Hall, 1974.
[2] C. M. RADER,: “Discrete convolutions via Mersenne
transforms. IEEE Trans. Comput., Vol. C-21, pp.
1269-1273, Dec. 1972.
[3] R. C. AGARWAL and C. S. BURRUS, “Number
theoretic transforms to implement fast digital
convolution”. Proc. IEEE, Vol. 63, pp. 550-560, Apr.
1975.
[4] R. C. AGARWAL and C. S. BURRUS, “Fast
convolution using Fermat number transforms with
applications to digital filtering”. IEEE Trans. On
Acoust. Speech. Signal Process. Vol. ASSP-22, pp.
87-97, 1974.
[5] J. B. MARTENS, “Number Theoretic Transforms for
the Calculation of Convolutions”. IEEE Trans. On
Acoust. Speech. Signal Process. Vol. ASSP-31, No.
04, pp. 969 –978, August 1983.
[6] E. DUBOIS, and A. N. VENETSANOPOULOS, “The
generalized discrete Fourier transform in rings of
algebraic integers. IEEE Trans. On Acoust. Speech
Signal Process.Vol. ASSP-28, pp. 169-175, (1980).
[7] C. M. RADER, “On the application of the number
theoretic transform methods of high-speed convolution
to two-dimensional filtering. IEEE Trans., pp. 575,
(1977).
[8] F. MARIR, “The Application of Number Theoretic
Transforms to Two-Dimensional Convolution and
Adaptive Filtering”. PhD Thesis, Newcastle
University, UK 1986.
[9] T. Toivonen and J. Heikkilä, “Video Filtering with
Fermat Number Theoretic Transforms Using Residue
Number System”, IEEE Trans. On circuits and
systems for video technology, VOL. 16, NO. 1,
January 2006.
[10] G. Madre, et al. “Linear predictive speech coding
using Fermat number transform”, the 4th EURASIP
Conference on video/image processing and multimedia
communications, Zagreb, Croatia,2-5 july 2003,.
[11] T. Conway, “Modified overlap technique using Fermat
and Mersenne transforms”, IEEE Trans. On circuits
and systems-II express briefs, VOL. 53, NO. 8, August
2006.
[12] R. M. Campello de Souza, et al., “Hartley number
theoretic transforms”, ISIT2001, Washington, DC,
June 24-29, 2001
Prentice Hall, 1974.
[2] C. M. RADER,: “Discrete convolutions via Mersenne
transforms. IEEE Trans. Comput., Vol. C-21, pp.
1269-1273, Dec. 1972.
[3] R. C. AGARWAL and C. S. BURRUS, “Number
theoretic transforms to implement fast digital
convolution”. Proc. IEEE, Vol. 63, pp. 550-560, Apr.
1975.
[4] R. C. AGARWAL and C. S. BURRUS, “Fast
convolution using Fermat number transforms with
applications to digital filtering”. IEEE Trans. On
Acoust. Speech. Signal Process. Vol. ASSP-22, pp.
87-97, 1974.
[5] J. B. MARTENS, “Number Theoretic Transforms for
the Calculation of Convolutions”. IEEE Trans. On
Acoust. Speech. Signal Process. Vol. ASSP-31, No.
04, pp. 969 –978, August 1983.
[6] E. DUBOIS, and A. N. VENETSANOPOULOS, “The
generalized discrete Fourier transform in rings of
algebraic integers. IEEE Trans. On Acoust. Speech
Signal Process.Vol. ASSP-28, pp. 169-175, (1980).
[7] C. M. RADER, “On the application of the number
theoretic transform methods of high-speed convolution
to two-dimensional filtering. IEEE Trans., pp. 575,
(1977).
[8] F. MARIR, “The Application of Number Theoretic
Transforms to Two-Dimensional Convolution and
Adaptive Filtering”. PhD Thesis, Newcastle
University, UK 1986.
[9] T. Toivonen and J. Heikkilä, “Video Filtering with
Fermat Number Theoretic Transforms Using Residue
Number System”, IEEE Trans. On circuits and
systems for video technology, VOL. 16, NO. 1,
January 2006.
[10] G. Madre, et al. “Linear predictive speech coding
using Fermat number transform”, the 4th EURASIP
Conference on video/image processing and multimedia
communications, Zagreb, Croatia,2-5 july 2003,.
[11] T. Conway, “Modified overlap technique using Fermat
and Mersenne transforms”, IEEE Trans. On circuits
and systems-II express briefs, VOL. 53, NO. 8, August
2006.
[12] R. M. Campello de Souza, et al., “Hartley number
theoretic transforms”, ISIT2001, Washington, DC,
June 24-29, 2001
Comment citer
TOUBA, M.; BENNIA, A .; TOUBA, S..
ON SOME RESULTS OF NUMBER THEORETIC TRANSFORM (NTT) -PERIODIC SIGNAL.
Courrier du Savoir, [S.l.], v. 13, mai 2014.
ISSN 1112-3338.
Disponible à l'adresse : >https://revues.univ-biskra.dz/index.php/cds/article/view/433>. Date de consultation : 22 déc. 2024
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